Before You Begin

Question #42471

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m = 4 \text{ kg}$ moving horizontally with a velocity $v_0 = 8 \text{ m/s}$ strikes a smooth wedge of mass $M = 5 \text{ kg}$ and inclination angle $\theta = 60^\circ$ . The wedge is initially at rest on a smooth horizontal surface. The collision is perfectly inelastic in the direction normal to the wedge surface (i.e., the particle does not bounce off the wedge but begins to slide along it immediately). Calculate the kinetic energy dissipated during the collision.

Options

A.
$60 \text{ J}$
B.
$\frac{160}{3} \text{ J}$
C.
$\frac{640}{9} \text{ J}$
D.
$96 \text{ J}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Wedge Constraint Logic|Impact Parameter Geometry|Vector Analysis

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of impulsive forces and geometric constraints.

A common trap is treating the collision using the standard reduced mass $\frac{mM}{m+M}$ along the normal (Option B), or assuming a 1D perfectly inelastic collision horizontally (Option C).

Students must recognize that the wedge's horizontal constraint alters the system's effective inertia in the normal direction.

By enforcing the kinematic constraint that the normal velocities of the particle and wedge must match post-collision, the correct effective mass $\mu_{\text{eff}} = \frac{mM}{M + m\sin^2\theta}$ is derived, leading to the correct energy dissipation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Wedge Constraint Logic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free